## Thursday, February 25, 2016

### Day 108: Scientific Notation Intro & Table->Equation for Quadratics

Students estimated the number of pages in the book Life of Pi. Although it looked 3/4 or 2/3 the size of the book Where the Sidewalk Ends, it was surprisingly deceiving more pages than students estimated.

Today students worked on the MARS FAL Estimating Length with Scientific Notation. The lesson starts with quite a bit of whiteboard. It gives students 3 expressions that all equal the same number. Some did not know the number. Students explained that 3 x 10^3 is like 10*10*10 which is a thousand and multiply that by 3. Then they had to justify why the other 3 expressions were equivalent. Students generalized that the exponent told you how many places to move the decimal, and which direction. If it were negative, the decimal moved to the left. I was pleasantly surprised that some students knew 10^-1 would divide it by 10, and 1 student knew it was equivalent to the reciprocal of 10, so he said it was 1/10.

Then students decided which of the expressions were in scientific notation. Most students thought they all were, some thought the one with the negative exponent was it because it was more complicated. Then students saw that 3 x 10^3 was the simplest looking, so it must be the most efficient. That was solid thinking. One student actually knew that it must be like a single digit before the decimal point. He had seen scientific notation in, where else, his science textbook.

Then we wrote down the definition below with the inequality and the plain English translation. Then students lastly decided which of 2 numbers in scientific notation was greater. They decided the number with -1 as an exponent was greater because -1 is greater than an exponent of -3. Then students showed me how to write the numbers in decimal form.

Students matched decimal notation to scientific notation. One match had it's decimal representation missing and another had its scientific notation missing. Students had trouble with 2 x 10^0 and thought it was 20. When I asked what the exponent tells you they said how to move the decimal. Well I asked, what would an exponent of 0 tell you to do? They said do nothing. So, what does that leave you with? 2. It actually made me deepen my understanding of raising to the 0 exponent and this was an intuitive way of looking at it.

Lastly, students matched real life objects to the measurements and glued it to their poster. Students that finished early were instructed to justify their choices. Students worked at varying paces. Tomorrow they will place arrows between the objects to show how you can multiply one quantity by a multiplier to get another.
 Instead of working in partners I had students work in groups of 4.
 Here were two of the equivalent expressions equal to 1,000.
 Here's the definition I had students copy down in their composition notebooks.
 In one class 2 students made the same mistake for 8x10^-3. They thought the 3 was in the numerator. Interestingly, he correctly interpreted 10^-1 as 1/10.
In accelerated, students worked on writing a quadratic equation from a table of values. Some graphed it, and some realized they could write the quadratic in factored form knowing its x-intercepts from the table. We didn't get time to go over the problem where they solve for the a value in a quadratic when given the x-intercepts on a graph. We will review this on Monday.

Students took a placement test for Mills High school and asked me questions about what the letter i meant. Apparently the placement test was adaptive because it gave them harder and harder problems if they were getting them right to see what questions were out of their range.

As you can see below, we did a participation quiz, and it definitely had students cooperating more than usual.

Tomorrow students will be assessed on graphing a quadratic in standard form. They'll start the last section on completing the square, finish it on Monday, and I believe we will work on Desmos Marbleslides Parabolas on Tuesday. I have to reserve the chrome carts, and I think I'll only reserve 1 so I can have a 2 to 1 ratio. I'd love for students to record themselves solving one of the challenges and uploading it on a blog, I'll just have to find time to pull them away from it, or just do it the next day.

 Participation quiz. Recording good behaviors, conversations, quotes, and some groups not cooperating.
 This was a hilarious quote. One student was falling behind, but he hilariously came up with this poetic quote. I had to give him props and write it on the board because it was so funny.